In a lithography process for manufacturing a semiconductor, a line edge roughness (hereinafter, referred to as “LER”) and a line width roughness (hereinafter, referred to as “LWR”) occur in a pattern formed on a wafer, especially in line-and-space patterns in which a plurality of line patterns are arranged at a specified interval, due to the effect of standing waves of light. The LER refers to the size of irregularities on a sidewall La of a line L, as shown in a cross sectional view of a wafer in FIG. 13. The LWR refers to the size of irregularities on both widthwise end portions, as shown in a plan view of a wafer in FIG. 14.
The standing waves of light contribute to the roughness. Light passing through a mask in an exposure process or light radiated to a resist is refracted or reflected, whereby light is interfered. If the interference light becomes strong or weak, ripple-shaped light patterns occur in the lines of the resist. In case of the transistors for nanoelectronics such as the 32 nm or 45 nm technology generation, the width of lines is 40 nm or 60 nm, which is much smaller than the wavelength of the exposure light. Therefore, roughness easily occurs by standing waves of light in the transistors for nanoelectronics.
It is important to control the LER and LWR in the lithography. Since the size of the line-and-space patterns is proportional to the gate length, the LER and LWR indicate the dimension variation in the gate pattern. Therefore, the irregular gate pattern has an influence on transistor performance. For example, roughness in the 45 nm technology generation should be suppressed to about 3 nm or less. However, roughness of 3 nm to 6 nm occurs in practice. Therefore, the lithography should be provided with the feedback or feed-forward of the result obtained by measuring the LER and the LWR. Roughness occurs in a circuit pattern after the etching process as well as in the resist pattern.
Currently, SEM (Scanning Electron Microscopy) observation has been used to measure the LER and the LWR. According to the SEM observation, secondary electrons emitted from a substrate upon irradiation of an electron beam form an image. The SEM is classified into a CD (Critical Dimension) SEM displaying an image of a pattern which is taken from above the wafer (see FIG. 14) and a cross-section SEM displaying a cross-sectional image of a pattern (see FIG. 13). The LWR is measured by the CD-SEM, while the LER is measured by the cross-section SEM. If the LER and LWR are measured by the SEM, roughness can be quantitatively determined by an image analysis.
On the other hand, a scatterometry method as another technique for measuring a pattern shape of a wafer is disclosed in, e.g., Patent Document 1. The scatterometry method uses an ellipsometer or reflectance spectrometer, by which light is irradiated on the wafer and a polarization state of the reflected light or a reflectivity of the wafer is measured. The polarization state and reflectivity of each wavelength region vary according to the pattern shape. Therefore, the pattern shape can be specified from the measured polarization state or reflectivity of each wavelength region by referring to the simulation results.
(Patent Document 1) Japanese Patent Application Publication No. 2005-33187 (Paragraphs [0067] to [0080])
However, since the SEM can measure only several square microns at a time, the measurement takes a long time. Further, the wafer is damaged by irradiation of the electron beam. Therefore, it is not suitable for measurement of practical devices.
Furthermore, in order to measure the LER using the cross-section SEM, the wafer has to be cut before the measurement. Thus cut wafer cannot be used as a chip, thereby deteriorating the production yield. Although the LER is related to the LWR, it is assumed that the causes are different. That is, even though the LWR has been measured, the LER cannot be estimated from the LWR.
The method for measuring roughness by using the SEM has the aforementioned drawbacks. The present inventor has attempted to use the scatterometry method for the measurement of roughness. However, although the pattern shape may be measured by using the present scatterometry method, it is difficult to measure roughness of the pattern according to the prior art. That is, since the pattern shape is measured only once at a specified location of the wafer and roughness is not much larger than the pattern shape, it is difficult to ascertain whether the variation in the obtained spectrum is due to roughness or it is due to the pattern shape.